The overall objective of this research is the development of techniques for the reconstruction of high-resolution, quantitative images that improve as well as extend the utility of ultrasound as a diagnostic tool in medicine. More specifically, the immediate goal is to develop the numerical methods and software necessary to obtain high-resolution, quantitative images of tissue using an experimental apparatus that has recently been developed at the University of Rochester. This project brings together expertise in computational optimization, inveerse problems, and instrumentation to address an important, practical problem in medical imaging.